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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Pylypiva, Oleksandra; Tymoshkevych, Larysa;

    The paper is devoted to inverse spectral problems for weighted graphs. We give the sharp upper bound for spectral reconstruction number of trees and unicyclic graphs. Роботу присвячено оберненим спектральним задачам для зважених графів. Наведено верхню оцінку спектрального відновлюючого числа для дерев та уніциклічних графів.

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    Mohyla Mathematical Journal
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Mohyla Mathematical ...arrow_drop_down
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      Mohyla Mathematical Journal
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  • Authors: Kozachok, Oleksandra;

    Randomization and probabilistic approach in the algorithms development occupy prominent place.Due to limited computing resources and complexity many tasks in some cases it’s impossible to obtain accurate results or it’s too costly, so the results may contain some uncertainty. There are also cases when the indeterminacy of the algorithm is its advantage, for example in cryptography problems, or a useful characteristic: in simulations of processes containing undefined parameters.In this paper, we consider the basic concepts and statements concerning randomized algorithms for checking numbers for simplicity, we present the necessary theorems. Рандомiзацiя та ймовiрнiсний пiдхiд у побудовi алгоритмiв займають помiтне мiсце. Через обмеженiсть обчислювальних ресурсiв та складнiсть багатьох задач у деяких випадках отримати точнi результати є неможливим або занадто витратним, тому результати можуть мiстити деяку невизначенiсть. Також у деяких випадках недетермiнованiсть алгоритму є його перевагою, наприклад у задачах криптографiї, або корисною характеристикою, як-от у симуляцiях процесiв, що мiстять невизначенi параметри.У цiй роботi ми розглядаємо основнi поняття та твердження, що стосуються рандомiзованих алгоритмiв перевiрки чисел на простоту, наводимо необхiднi теореми.

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  • Authors: Oliynyk, Andriy; Oliynyk, Bogdana;

    The paper is dedicated to the memory of an outstanding ukrainian mathematician and teacher, one of the founders of Kyiv school of representation theory and ring theory, professor of Taras Shevchenko National University of Kyiv Volodymyr Vasylovych Kyrychenko. Volodymyr Vasylovych was born in 1942 in Penza. He graduated Kyiv University with honors in 1964. He defended his PhD thesis “Representations of hereditary, completely decomposable and Bass orders” under the supervision of D.K. Faddeev. He defended his habilitation “Modules and structural theory of rings” in 1986. He started to work at Kyiv University as an assistant of the Algebra and Mathematical Logic Department in 1967. Since then he served as an Associate Professor and Professor of the Algebra and Mathematical Logic Department. He was the head of the Geometry Department from 1988 till 2016. His main scientific results lay in the field of structural ring theory. In particular, he introduced the notion of the quiver for some special casses of rings and developed the structural theory of hereditary semiserial semidistributive rings. He is the author of about 250 scientific papers and 5 fundamental monographies. In his monographies the theory of semiperfect rings is presented by means of correspond- ing quivers. The monography “Finite dimensional algebras” written jointly with professor Y. Drozd is regarded one of the classical works in algebra and translated from Russian to Chineese, English and Spanish. He was an outstanding teacher and 36 PhD thesis were defended under his supervision. His lectures on analytical geometry and ring theory were always top ranked among students. Professor Kyrychenko was one of the founders of the journal “Algebra and Discrete Mathematics”. He was an editor of a couple of mathematical journals. In 1997 he was one of the founders of the series of international algebraic conferences in Ukraine that were conducted every two years. Since that he was one of the main organizers of each of them. Статтю присвячено пам’ятi видатного українського математика i педагога, одного iз засновникiв київської школи теорiї зображень i теорiї кiлець, професора Київського нацiонального унiверситету iменi Тараса Шевченка Володимира Васильовича Кириченка.

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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Ryszard Frankiewicz;

    Remarks on my algebraic problem of determining similarities between certain quotient boolean algebras.In this paper we survey results about quotient boolean algebras of type P(κ)/fin(κ) and condition for them to be or not to be isomorphic for different cardinals κ. Our consideration have their root in the classical result of Parovicenko and a less classical, nevertheless really considerable result about non-existence of P-points by S Shellah. Our main point of interest are the algebras P(ω)/fin(ω) and P(ℵ1)/fin(ℵ1). У цій статті ми розглядаємо результати щодо факторних булевих алгебр типу P(κ)/fin(κ) та відповідаємо на запитання, чи є булеві алгебри ізоморфними для різних кардиналів κ. Наші міркування беруть своє коріння з класичного результату Паровіченка і менш класичного, проте дійсно вагомого результату про відсутність P-точок за С. Шелах. Головна мета нашої статті - це розгляд алгебр P(ω)/fin(ω) i P(ℵ1)/fin(ℵ1).

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    Mohyla Mathematical Journal
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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    Authors: Slawomir Kusinski;

    In this paper we are exploring application of fusion lemma - a result about perfect trees, having its origin in forcing theory - to some special cases of a problem proposed by Leo Harrington in a book Analytic Sets. In all generality the problem ask whether given a sequence of functions from Rω to [0; 1] one can find a subsequence of it that is pointwise convergent on a product of perfect subsets of R. We restrict our attention mainly to binary functions on the Cantor set as well as outline the possible direction of generalization of result to other topological spaces and different notions of measurablity. У цій статті ми досліджуємо застосування леми про злиття - результат про ідеальні дерева, що походить від теорії примусу - до деяких особливих випадків проблеми, запропонованої Лео Харінгтоном у книзі "Аналітичні множини". У загальному випадку проблема полягає у тому, чи можна знайти для послідовності функцій від Rω до [0; 1] її підпослідовність, яка поточково збіжна до добутку ідеальних підмножин R. Ми розглядатимемо головним чином бінарні функції на множині Кантора, а також окреслимо можливий напрямок узагальнення результату на інші топологічні простори та різні поняття вимірності.

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  • Authors: Lemeshko, Elizabeth;

    Nowadays, science is characterized by needs of the study of various complex processes and phenomena’s. Today’s research of complex and dynamical systems is one of the most advanced ways of research and evolution of the modern world. Models of biology and ecology, physical models, various economic and social models are typical examples of dynamic systems.The concept of an interactive complex system in modern science is a main tool for construction of mathematical models for solving modern civilization problems and development. The dynamical systems approach to conflict is relatively new, but it has beginning in different research fields. Theory of dynamic systems helps us to understand the experiments, build the mathematical model of iterations and examine behavior and relations between opponents, like distribution of resources and territory, population growing etc.This is a challenging problem of finding and achieving a compromise state for opponents on a common territory has different options to define the task and to choose conflict interaction. In 2016, the monograph by V. Koshmanenko where was introduced new approach for dynamic system of conflict that based on interactions of the opponents in the form probability distribution in the disputed area was published. In particular, presented the concept of a complex dynamic system with attractive interaction.The relevance of this research is improving new dynamical system and researching for a new application of abstract models in everyday life. In this paper briefly fundamentals of the theory of dynamical systems described and the theorem on the existence of a equilibrium state in a the new, perspective for research, dynamical system with attractive interaction in terms of probability distributions (measures) and their densities, formulated and proved. Поняття iнтерактивної складної системи є основним iнструментом у побудовi математичних моделей для розв’язання сучасних проблем цивiлiзацiйного розвитку. Таким, зокрема, є поняття складної динамiчної системи з притягальною взаємодiєю. Проблема пошуку та досягнення компромiсного стану для опонентiв на спiльнiй територiї iснування має рiзнi варiанти постановки задачi i вибору конфлiктної взаємодiї. У цiй роботi сформульовано та доведено теорему про iснування граничного стану в динамiчнiй системi з притягальною взаємодiєю в термiнах щiльностей.

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  • Authors: Mytnyk, Yuriy; Kashpirovski, Oleksii; Oliynyk, Bogdana;

    The article is devoted to the 150th anniversary of the birth of outstanding Ukrainian mathematician Georgy Feodosiyovych Voronoi who has woldwide recognition. Georgy Voronoi was born on April 28, 1868 in the small town of Zhuravka near Chernihiv. Georgy Voronoi first followed school at Berdyansk and later attended the Pryluky gymnasium from which he graduated in 1885. His first scientific paper was entitled "Decomposition of the polynomials on factors based on the properties of the roots of quadratic equation" published in Elementary Math. J. in Kyiv in 1885. Latter he studied in the University of St Petersburg on the Faculty of Physics and Mathematics. He was awarded a Master’s Degree in 1894 for the dissertation on the algebraic integers associated with the roots of an irreducible cubic equation. Andrey Markov was his supervisor. He worked as math professor at the University of Warsaw and published a number of scientific papers with significant results. He wrote his doctoral thesis on algorithms for continued fractions. The main scientific results of Georgy Voronoi were published in his papers "Sur quelques propriet´ es des formes quadratiques positives´ parfaites" and "Recherches sur les paralleloedres primitifs". In the last of them Georgy Voronoi introduced mathematical objects that are nowadays called Voronoi diagrams or Voronoi tessellations. Voronoi diagram is a partitioning of a plane into cells based on the distance to points in a specific subset of the plane. Nowadays Voronoi diagrams are one of the main objects of investigation in computational geometry. They are used in robotics, navigation systems, ecology, economic models, architecture, and clothing design, etc. There are many generalizations of Voronoi diagrams. We describe his life path and significant dates and events in his life. We consider also Georgy Voronoi’s main mathematical results and publications. Статтю присвячено 150-й рiчницi вiд дня народження видатного українського математика Георгiя Феодосiйовича Вороного. Описано його життєвий шлях, основнi математичнi результати i публiкацiї.

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    Authors: Tymoshkevych, Larysa; Kohut, Mariia;

    The structure of infinite Coxeter graphs whose largest eigenvalue belongs to the interval from √√5 + 2 to 3 3/√2] is investigated. In particular, such a graph is a tree, can have at most one label greater than 3 on its edges and such label does not exceed 6, can have only vertices with degree strictly less than 5, and among edges which are incident with vertex with degree 4 can be only one that is not incident with leaf. A number of other properties are also given for infinite Coxeter graphs with largest eigenvalue in the specified interval. Досліджено структуру зліченних графів Кокстера зі значенням індексу в проміжку від √√5 + 2 до 3/√2. Зокрема, такі графи є деревами, можуть мати щонайбільше одну позначку на ребрах, більшу за 3, і такі позначки не перевищують 6, можуть мати лише вершини степеня строго меншого за 5, і серед ребер, інцидентних вершині степеня 4, може бути лише одне, що інцидентне не висячій вершині. Також наведено ряд інших властивостей зліченних графів Кокстера з індексами у квазаному проміжку.

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  • Authors: Olshevska, Vita;

    The Sylow 2-subgroups of symmetric groups was described by Leo Kaluzhnin. He presented the elements of these groups as a tables, i.e. the ordered sets of polynomials of a certain form. The Sylow 2-subgroups of symmetric groups was studied by V. Sushchanskii, Yu. Dmytruk, A. Slupik and other mathematicians. In this paper the Sylow 2-subgroups of alternating groups are characterized. The system of computer algebra GAP was used for this characterization.System of computer algebra GAP is the most popular frequency of references in scientific publications and the number of links on Internet pages. Its popularity is conditioned by accessibility, large set of functions and packages for calculations in theoretical and mathematical sciences, clarity and ease to use. At the moment, it is an auxiliary tool for working with groups, finite fields, algebraic extension of fields, Galois group, polynomials of many variables, rational functions, vectors, matrices, etc. In addition, this list is supplemented every day.The CMG-program (Check Minimal Generators) is provided in this article. It is created using the GAP system and is used for calculations in Sylow 2-subgroups of alternating groups. The main task of the program is to check whether some set S can be a system of generators of the Sylow 2-subgroup of alternating group. The program are used for groups Syl2(A8) and Syl2(A16). In addition, the commutator and the factor subgroup of these groups are investigated. It is shown that each element of the commutator subgroup of the group Syl2(A8) is commutator in this group. Moreover, the subgroup of order 4 of the commutator of the group Syl2(A8) is described. Also, this program checks whether the commutators and the factor groups of groups Syl2(A8) and Syl2(A16) are Abelian. У статтi наведено алгоритм перевiрки, чи є певна множина елементiв S мiнiмальною системою твiрних для силовської 2-пiдгрупи знакозмiнної групи Syl2(A2n), за допомогою системи комп’ютерної алгебри GAP. Для невеликих n (n = 3 i n = 4) проведено обчислення за допомогою цього алгоритму. Зокрема, перевiрено абелевiсть, пораховано потужнiсть та кiлькiсть елементiв мiнiмальної системи твiрних комутантiв у кожнiй з груп Syl2(A8), Syl2(A16) та фактор-групах цих силовських 2-пiдгруп по комутанту.

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    Authors: Oleg Kravchuk; Galyna Kriukova;

    In this work, a generalized scheme of regularization of inverse problems is considered, where a priori knowledge about the smoothness of the solution is given by means of some self-adjoint operator in the solution space. The formulation of the problem is considered, namely, in addition to the main inverse problem, an additional problem is defined, in which the solution is the right-hand side of the equation. Thus, for the regularization of the main inverse problem, an additional inverse problem is used, which brings information about the smoothness of the solution to the initial problem. This formulation of the problem makes it possible to use operators of high complexity for regularization of inverse problems, which is an urgent need in modern machine learning problems, in particular, in image processing problems. The paper examines the approximation error of the solution of the initial problem using an additional problem. У цій роботі розглянуто узагальнену схему регуляризації обернених задач, де апріорне знання про гладкість розв'язку дано за допомогою деякого самоспряженого оператора в просторі розв'язків. Розглянуто постановку задачі, коли окрім основної оберненої задачі визначено додаткову задачу, в якій шуканий розв'язок є правою частиною рівняння. Таким чином, для регуляризації основної оберненої задачі використовується додаткова обернена задача, яка привносить до початкової задачі інформацію про гладкість розв'язку. Така постановка задачі дає можливість використовувати оператори високої складності для регуляризації обернених задач, що є нагальною потребою в сучасних задачах машинного навчання, зокрема, в задачах обробки зображень. В роботі досліджено похибку апроксимації розв'язку початкової задачі за допомогою додаткової задачі.

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64 Research products for Mohyla Mathematical Journal
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    Authors: Pylypiva, Oleksandra; Tymoshkevych, Larysa;

    The paper is devoted to inverse spectral problems for weighted graphs. We give the sharp upper bound for spectral reconstruction number of trees and unicyclic graphs. Роботу присвячено оберненим спектральним задачам для зважених графів. Наведено верхню оцінку спектрального відновлюючого числа для дерев та уніциклічних графів.

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  • Authors: Kozachok, Oleksandra;

    Randomization and probabilistic approach in the algorithms development occupy prominent place.Due to limited computing resources and complexity many tasks in some cases it’s impossible to obtain accurate results or it’s too costly, so the results may contain some uncertainty. There are also cases when the indeterminacy of the algorithm is its advantage, for example in cryptography problems, or a useful characteristic: in simulations of processes containing undefined parameters.In this paper, we consider the basic concepts and statements concerning randomized algorithms for checking numbers for simplicity, we present the necessary theorems. Рандомiзацiя та ймовiрнiсний пiдхiд у побудовi алгоритмiв займають помiтне мiсце. Через обмеженiсть обчислювальних ресурсiв та складнiсть багатьох задач у деяких випадках отримати точнi результати є неможливим або занадто витратним, тому результати можуть мiстити деяку невизначенiсть. Також у деяких випадках недетермiнованiсть алгоритму є його перевагою, наприклад у задачах криптографiї, або корисною характеристикою, як-от у симуляцiях процесiв, що мiстять невизначенi параметри.У цiй роботi ми розглядаємо основнi поняття та твердження, що стосуються рандомiзованих алгоритмiв перевiрки чисел на простоту, наводимо необхiднi теореми.

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  • Authors: Oliynyk, Andriy; Oliynyk, Bogdana;

    The paper is dedicated to the memory of an outstanding ukrainian mathematician and teacher, one of the founders of Kyiv school of representation theory and ring theory, professor of Taras Shevchenko National University of Kyiv Volodymyr Vasylovych Kyrychenko. Volodymyr Vasylovych was born in 1942 in Penza. He graduated Kyiv University with honors in 1964. He defended his PhD thesis “Representations of hereditary, completely decomposable and Bass orders” under the supervision of D.K. Faddeev. He defended his habilitation “Modules and structural theory of rings” in 1986. He started to work at Kyiv University as an assistant of the Algebra and Mathematical Logic Department in 1967. Since then he served as an Associate Professor and Professor of the Algebra and Mathematical Logic Department. He was the head of the Geometry Department from 1988 till 2016. His main scientific results lay in the field of structural ring theory. In particular, he introduced the notion of the quiver for some special casses of rings and developed the structural theory of hereditary semiserial semidistributive rings. He is the author of about 250 scientific papers and 5 fundamental monographies. In his monographies the theory of semiperfect rings is presented by means of correspond- ing quivers. The monography “Finite dimensional algebras” written jointly with professor Y. Drozd is regarded one of the classical works in algebra and translated from Russian to Chineese, English and Spanish. He was an outstanding teacher and 36 PhD thesis were defended under his supervision. His lectures on analytical geometry and ring theory were always top ranked among students. Professor Kyrychenko was one of the founders of the journal “Algebra and Discrete Mathematics”. He was an editor of a couple of mathematical journals. In 1997 he was one of the founders of the series of international algebraic conferences in Ukraine that were conducted every two years. Since that he was one of the main organizers of each of them. Статтю присвячено пам’ятi видатного українського математика i педагога, одного iз засновникiв київської школи теорiї зображень i теорiї кiлець, професора Київського нацiонального унiверситету iменi Тараса Шевченка Володимира Васильовича Кириченка.

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    Authors: Ryszard Frankiewicz;

    Remarks on my algebraic problem of determining similarities between certain quotient boolean algebras.In this paper we survey results about quotient boolean algebras of type P(κ)/fin(κ) and condition for them to be or not to be isomorphic for different cardinals κ. Our consideration have their root in the classical result of Parovicenko and a less classical, nevertheless really considerable result about non-existence of P-points by S Shellah. Our main point of interest are the algebras P(ω)/fin(ω) and P(ℵ1)/fin(ℵ1). У цій статті ми розглядаємо результати щодо факторних булевих алгебр типу P(κ)/fin(κ) та відповідаємо на запитання, чи є булеві алгебри ізоморфними для різних кардиналів κ. Наші міркування беруть своє коріння з класичного результату Паровіченка і менш класичного, проте дійсно вагомого результату про відсутність P-точок за С. Шелах. Головна мета нашої статті - це розгляд алгебр P(ω)/fin(ω) i P(ℵ1)/fin(ℵ1).

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    Authors: Slawomir Kusinski;

    In this paper we are exploring application of fusion lemma - a result about perfect trees, having its origin in forcing theory - to some special cases of a problem proposed by Leo Harrington in a book Analytic Sets. In all generality the problem ask whether given a sequence of functions from Rω to [0; 1] one can find a subsequence of it that is pointwise convergent on a product of perfect subsets of R. We restrict our attention mainly to binary functions on the Cantor set as well as outline the possible direction of generalization of result to other topological spaces and different notions of measurablity. У цій статті ми досліджуємо застосування леми про злиття - результат про ідеальні дерева, що походить від теорії примусу - до деяких особливих випадків проблеми, запропонованої Лео Харінгтоном у книзі "Аналітичні множини". У загальному випадку проблема полягає у тому, чи можна знайти для послідовності функцій від Rω до [0; 1] її підпослідовність, яка поточково збіжна до добутку ідеальних підмножин R. Ми розглядатимемо головним чином бінарні функції на множині Кантора, а також окреслимо можливий напрямок узагальнення результату на інші топологічні простори та різні поняття вимірності.

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  • Authors: Lemeshko, Elizabeth;

    Nowadays, science is characterized by needs of the study of various complex processes and phenomena’s. Today’s research of complex and dynamical systems is one of the most advanced ways of research and evolution of the modern world. Models of biology and ecology, physical models, various economic and social models are typical examples of dynamic systems.The concept of an interactive complex system in modern science is a main tool for construction of mathematical models for solving modern civilization problems and development. The dynamical systems approach to conflict is relatively new, but it has beginning in different research fields. Theory of dynamic systems helps us to understand the experiments, build the mathematical model of iterations and examine behavior and relations between opponents, like distribution of resources and territory, population growing etc.This is a challenging problem of finding and achieving a compromise state for opponents on a common territory has different options to define the task and to choose conflict interaction. In 2016, the monograph by V. Koshmanenko where was introduced new approach for dynamic system of conflict that based on interactions of the opponents in the form probability distribution in the disputed area was published. In particular, presented the concept of a complex dynamic system with attractive interaction.The relevance of this research is improving new dynamical system and researching for a new application of abstract models in everyday life. In this paper briefly fundamentals of the theory of dynamical systems described and the theorem on the existence of a equilibrium state in a the new, perspective for research, dynamical system with attractive interaction in terms of probability distributions (measures) and their densities, formulated and proved. Поняття iнтерактивної складної системи є основним iнструментом у побудовi математичних моделей для розв’язання сучасних проблем цивiлiзацiйного розвитку. Таким, зокрема, є поняття складної динамiчної системи з притягальною взаємодiєю. Проблема пошуку та досягнення компромiсного стану для опонентiв на спiльнiй територiї iснування має рiзнi варiанти постановки задачi i вибору конфлiктної взаємодiї. У цiй роботi сформульовано та доведено теорему про iснування граничного стану в динамiчнiй системi з притягальною взаємодiєю в термiнах щiльностей.

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  • Authors: Mytnyk, Yuriy; Kashpirovski, Oleksii; Oliynyk, Bogdana;

    The article is devoted to the 150th anniversary of the birth of outstanding Ukrainian mathematician Georgy Feodosiyovych Voronoi who has woldwide recognition. Georgy Voronoi was born on April 28, 1868 in the small town of Zhuravka near Chernihiv. Georgy Voronoi first followed school at Berdyansk and later attended the Pryluky gymnasium from which he graduated in 1885. His first scientific paper was entitled "Decomposition of the polynomials on factors based on the properties of the roots of quadratic equation" published in Elementary Math. J. in Kyiv in 1885. Latter he studied in the University of St Petersburg on the Faculty of Physics and Mathematics. He was awarded a Master’s Degree in 1894 for the dissertation on the algebraic integers associated with the roots of an irreducible cubic equation. Andrey Markov was his supervisor. He worked as math professor at the University of Warsaw and published a number of scientific papers with significant results. He wrote his doctoral thesis on algorithms for continued fractions. The main scientific results of Georgy Voronoi were published in his papers "Sur quelques propriet´ es des formes quadratiques positives´ parfaites" and "Recherches sur les paralleloedres primitifs". In the last of them Georgy Voronoi introduced mathematical objects that are nowadays called Voronoi diagrams or Voronoi tessellations. Voronoi diagram is a partitioning of a plane into cells based on the distance to points in a specific subset of the plane. Nowadays Voronoi diagrams are one of the main objects of investigation in computational geometry. They are used in robotics, navigation systems, ecology, economic models, architecture, and clothing design, etc. There are many generalizations of Voronoi diagrams. We describe his life path and significant dates and events in his life. We consider also Georgy Voronoi’s main mathematical results and publications. Статтю присвячено 150-й рiчницi вiд дня народження видатного українського математика Георгiя Феодосiйовича Вороного. Описано його життєвий шлях, основнi математичнi результати i публiкацiї.

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    Authors: Tymoshkevych, Larysa; Kohut, Mariia;

    The structure of infinite Coxeter graphs whose largest eigenvalue belongs to the interval from √√5 + 2 to 3 3/√2] is investigated. In particular, such a graph is a tree, can have at most one label greater than 3 on its edges and such label does not exceed 6, can have only vertices with degree strictly less than 5, and among edges which are incident with vertex with degree 4 can be only one that is not incident with leaf. A number of other properties are also given for infinite Coxeter graphs with largest eigenvalue in the specified interval. Досліджено структуру зліченних графів Кокстера зі значенням індексу в проміжку від √√5 + 2 до 3/√2. Зокрема, такі графи є деревами, можуть мати щонайбільше одну позначку на ребрах, більшу за 3, і такі позначки не перевищують 6, можуть мати лише вершини степеня строго меншого за 5, і серед ребер, інцидентних вершині степеня 4, може бути лише одне, що інцидентне не висячій вершині. Також наведено ряд інших властивостей зліченних графів Кокстера з індексами у квазаному проміжку.

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    Mohyla Mathematical Journal
    Article . 2022
    License: CC BY
    Data sources: Crossref
    Mohyla Mathematical Journal
    Article . 2022
    License: CC BY
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      Mohyla Mathematical Journal
      Article . 2022
      License: CC BY
      Data sources: Crossref